### Abstract

Original language | Undefined |
---|---|

Article number | 10.1239/jap/1014842840 |

Pages (from-to) | 835-849 |

Number of pages | 14 |

Journal | Journal of applied probability |

Volume | 2000 |

Issue number | 37 |

DOIs | |

Publication status | Published - 2000 |

### Keywords

- invariant vector
- EWI-12851
- transition function
- METIS-140634
- Transient behaviour
- IR-62348
- Chain sequence
- Absorption probability

### Cite this

*Journal of applied probability*,

*2000*(37), 835-849. [10.1239/jap/1014842840]. https://doi.org/10.1239/jap/1014842840

}

*Journal of applied probability*, vol. 2000, no. 37, 10.1239/jap/1014842840, pp. 835-849. https://doi.org/10.1239/jap/1014842840

**Families of birth-death processes with similar time-dependent behaviour.** / Lenin, R.B.; Parthasarathy, P.R.; Scheinhardt, Willem R.W.; van Doorn, Erik A.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Families of birth-death processes with similar time-dependent behaviour.

AU - Lenin, R.B.

AU - Parthasarathy, P.R.

AU - Scheinhardt, Willem R.W.

AU - van Doorn, Erik A.

PY - 2000

Y1 - 2000

N2 - We consider birth-death processes taking values in N ≡ {0,1,... }, but allow the death rate in state 0 to be positive, so that escape from N is possible. Two such processes with transition functions { pij(t) } and { ̃pij(t) } are said to be similar if, for all i, j ∈ N, there are constants cij such that ̃pij(t) = cijpij(t) for all t ≥ 0. We determine conditions on the birth and death rates of a birth-death process for the process to be a member of a family of similar processes, and we identify the members of such a family. These issues are also resolved in the more general setting in which the two processes are called similar if there are constants cij and ν such that ̃pij(t) = cijeνtpij(t) for all t ≥ 0.

AB - We consider birth-death processes taking values in N ≡ {0,1,... }, but allow the death rate in state 0 to be positive, so that escape from N is possible. Two such processes with transition functions { pij(t) } and { ̃pij(t) } are said to be similar if, for all i, j ∈ N, there are constants cij such that ̃pij(t) = cijpij(t) for all t ≥ 0. We determine conditions on the birth and death rates of a birth-death process for the process to be a member of a family of similar processes, and we identify the members of such a family. These issues are also resolved in the more general setting in which the two processes are called similar if there are constants cij and ν such that ̃pij(t) = cijeνtpij(t) for all t ≥ 0.

KW - invariant vector

KW - EWI-12851

KW - transition function

KW - METIS-140634

KW - Transient behaviour

KW - IR-62348

KW - Chain sequence

KW - Absorption probability

U2 - 10.1239/jap/1014842840

DO - 10.1239/jap/1014842840

M3 - Article

VL - 2000

SP - 835

EP - 849

JO - Journal of applied probability

JF - Journal of applied probability

SN - 0021-9002

IS - 37

M1 - 10.1239/jap/1014842840

ER -